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0.0

Jan 16, 2021
01/21

by
Nikolas Götze (HobbyTV)

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Customized version of http://www.thingiverse.com/thing:1997335 Created with Customizer! http://www.thingiverse.com/apps/customizer/run?thing_id=1997335

Topics: customized, stl, Signs & Logos, thingiverse

0
0.0

Apr 17, 2021
04/21

by
Michael Götze (StavroX)

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Yet another filament holder. Can be fixed to the table with simple screws.

Topics: filament_spool_holder, filament_holder, thingiverse, stl, 3D Printer Accessories

68
68

Sep 23, 2013
09/13

by
Nikita Alexeev; Friedrich Götze; Alexander Tikhomirov

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We consider products of independent large random rectangular matrices with independent entries. The limit distribution of the expected empirical distribution of singular values of such products is computed. The distribution function is described by its Stieltjes transform, which satisfies some algebraic equation. In the particular case of square matrices we get a well-known distribution which moments are Fuss-Catalan numbers.

Source: http://arxiv.org/abs/1012.2586v2

51
51

Sep 21, 2013
09/13

by
S. G. Bobkov; G. P. Chistyakov; F. Götze

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An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is studied via properties of the Fisher information along convolutions.

Source: http://arxiv.org/abs/1204.6650v1

202
202

Oct 23, 2014
10/14

by
Wutka, Annika; Palagani, Vindhya; Barat, Samarpita; Chen, Xi; El Khatib, Mona; Gotze, Julian; Belahmer, Hanane; Zender, Steffen; Bozko, Przemyslaw; Malek, Nisar P.; Plentz, Ruben R.

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This article is from PLoS ONE , volume 9 . Abstract Capsaicin, the most abundant pungent molecule produced by pepper plants, represents an important ingredient in spicy foods consumed throughout the world. Studies have shown that capsaicin can relieve inflammation and has anti-proliferative effects on various human malignancies. Cholangiocarcinoma (CC) is a cancer disease with rising incidence. The prognosis remains dismal with little advance in treatment. The aim of the present study is to...

Source: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3991659

Emilio's Historical Pictures

378
378

Sep 15, 2019
09/19

by
Wilhelm GRÜNING - Tenor, Geraldine FARRAR - Sopran, Marie GÖTZE - Alt, Robert PHILLIP - Tenor., Marie DIETRICH - Sopran

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Faces of Historical Opera (Collection of Singer's Photos) Wilhelm GRÜNING - Tenor Photo 10 Wilhelm GRÜNING - Tenor Postkarte: als "Rienzi" hoch zu Pferd Verlag: Hermann Leiser vormals Louis Blumenthal, Nr. 3317 Photographer: F.O. Lundt Date: ca. 1907 Back of the Photo: unused postcard, not scanned Photo 15 Wilhelm GRÜNING - Tenor Postkarte: seitlich sitzend im Sessel mit geschnitzter Armlehne. Autographed "Wilhelm Grüning 1903" Verlag: not given Photographer: not given...

Topics: tenor, Grüning, Faces of Hisatorical Opera, Verlag Hermann Leiser vormals Louis Blumenthal, Emil...

9
9.0

Jun 28, 2018
06/18

by
O. Götze; J. Richter; R. Zinke; D. J. J. Farnell

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We apply the coupled cluster method to high orders of approximation and exact diagonalizations to study the ground-state properties of the triangular-lattice spin-$s$ Heisenberg antiferromagnet. We calculate the fundamental ground-state quantities, namely, the energy $e_0$, the sublattice magnetization $M_{\rm sub}$, the in-plane spin stiffness $\rho_s$ and the in-plane magnetic susceptibility $\chi$ for spin quantum numbers $s=1/2, 1, \ldots, s_{\rm max}$, where $s_{\rm max}=9/2$ for $e_0$ and...

Topics: Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1508.06254

51
51

Sep 23, 2013
09/13

by
Nikita Alexeev; Friedrich Götze; Alexander Tikhomirov

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We consider powers of random matrices with independent entries. Let $X_{ij}, i,j\ge 1$, be independent complex random variables with $\E X_{ij}=0$ and $\E |X_{ij}|^2=1$ and let $\mathbf X$ denote an $n\times n$ matrix with $[\mathbf X]_{ij}=X_{ij}$, for $1\le i, j\le n$. Denote by $s_1^{(m)}\ge...\ge s_n^{(m)}$ the singular values of the random matrix $\mathbf W:={n^{-\frac m2}} \mathbf X^m$ and define the empirical distribution of the squared singular values by $$ \mathcal...

Source: http://arxiv.org/abs/1012.2743v1

6
6.0

Nov 21, 2019
11/19

by
Frieda Langendorff; Robert Vomscheidt; Karl Gotze

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The size of the stylii used to transfer this record is 40. This record was digitized at 74 revolutions per minute.

4
4.0

Jun 30, 2018
06/18

by
Jasper S. Krauser; Jannes Heinze; S. Götze; M. Langbecker; N. Fläschner; Liam Cook; Thomas. M. Hanna; Eite Tiesinga; Klaus Sengstock; Christoph Becker

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Magnetically-tunable Feshbach resonances are an indispensable tool for experiments with atomic quantum gases. We report on twenty thus far unpublished Feshbach resonances and twenty one further probable Feshbach resonances in spin mixtures of ultracold fermionic 40 K with temperatures well below 100 nK. In particular, we locate a broad resonance at B=389.6 G with a magnetic width of 26.4 G. Here 1 G=10^-4 T. Furthermore, by exciting low-energy spin waves, we demonstrate a novel means to...

Topics: Quantum Gases, Condensed Matter

Source: http://arxiv.org/abs/1701.02085

2
2.0

Jun 28, 2018
06/18

by
Yulia S. Eliseeva; Friedrich Götze; Andrei Yu. Zaitsev

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Let $X,X_1,\ldots,X_n$ be independent identically distributed random variables. In this paper we study the behavior of concentration functions of weighted sums $\sum_{k=1}^{n} X_k a_k$ with respect to the arithmetic structure of coefficients~$a_k$ in the context of the Littlewood--Offord problem. Concentration results of this type received renewed interest in connection with distributions of singular values of random matrices. Recently, Tao and Vu proposed an Inverse Principle in the...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1512.02938

2
2.0

Jun 30, 2018
06/18

by
F. Götze; A. N. Tikhomirov

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Let $\mathbf X=(X_{jk})_{j,k=1}^n$ denote a Hermitian random matrix with entries $X_{jk}$, which are independent for $1\le j\le k\le n$. We consider the rate of convergence of the empirical spectral distribution function of the matrix $\mathbf W=\frac1{\sqrt n}\mathbf X$ to the semi-circular law assuming that $\mathbf E X_{jk}=0$, $\mathbf E X_{jk}^2=1$ and uniformly bounded eight moments. By means of a recursion argument it is shown that the Kolmogorov distance between the empirical spectral...

Topics: Probability, Mathematics, Mathematical Physics

Source: http://arxiv.org/abs/1407.2780

4
4.0

Jun 30, 2018
06/18

by
K. Götze; D. Aoki; F. Lévy-Bertrand; H. Harima; I. Sheikin

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We report high field de Haas-van Alphen (dHvA) effect measurements in CeRh$_2$Si$_2$ both below and above the first-order 26 T metamagnetic transition from an antiferromagnetic to a polarized paramagnetic state. The dHvA frequencies observed above the transition are much higher than those observed below, implying a drastic change of the Fermi-surface size. The dHvA frequencies above the transition and their angular dependence are in good agreement with band-structure calculations for...

Topics: Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1704.02139

2
2.0

Jun 30, 2018
06/18

by
Johannes Richter; Oliver Götze

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The existence of a spin-liquid ground state of the $s=1/2$ Heisenberg kagome antiferromagnet (KAFM) is well established. Meanwhile, also for the $s=1$ Heisenberg KAFM evidence for the absence of magnetic long-range order (LRO) was found. Magnetic LRO in Heisenberg KAFMs can emerge by increasing the spin quantum number $s$ to $s>1$ and for $s=1$ by an easy-plane anisotropy. In the present paper we discuss the route to magnetic order in $s=1/2$ KAFMs by including an isotropic interlayer...

Topics: Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1704.06809

2
2.0

Jun 29, 2018
06/18

by
Friedrich Götze; Anna Gusakova

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In 1970 A. Baker and W. Schmidt introduced regular systems of numbers and vectors, showing that the set of real algebraic numbers forms a regular system on any fixed interval. This fact was used to prove several important results in the metric theory of transcendental numbers. In this paper the concept of a regular system is applied to the set of algebraic integers $\alpha$ of height $\leq Q$ in intervals of length depending on $Q$.

Topics: Number Theory, Mathematics

Source: http://arxiv.org/abs/1602.01630

4
4.0

Jun 30, 2018
06/18

by
The CALICE Collaboration; B. Bilki; J. Repond; J. Schlereth; L. Xia; Z. Deng; Y. Li; Y. Wang; Q. Yue; Z. Yang; G. Eigen; P. Cornebise; Ph. Doublet; F. Dulucq; M. Faucci-Giannelli; J. Fleury; T. Frisson; B. Kégl; N. van der Kolk; H. Li; G. Martin-Chassard; Y. Mikami; F. Richard; Ch. de la Taille; R. Pöschl; L. Raux; J. Rouëné; N. Seguin-Moreau; M. Anduze; V. Balagura; E. Becheva; V. Boudry; T. Price; J-C. Brient; R. Cornat; M. Frotin; F. Gastaldi; F. Magniette; A. Matthieu; P. Mora de...

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A detailed study of hadronic interactions is presented using data recorded with the highly granular CALICE silicon-tungsten electromagnetic calorimeter. Approximately 350,000 selected negatively charged pion events at energies between 2 and 10 GeV have been studied. The predictions of several physics models available within the Geant4 simulation tool kit are compared to this data. A reasonable overall description of the data is observed; the Monte Carlo predictions are within 20% of the data,...

Topics: Physics, High Energy Physics - Experiment, Instrumentation and Detectors

Source: http://arxiv.org/abs/1411.7215

1
1.0

Jan 16, 2021
01/21

by
Nikolas Götze (HobbyTV)

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Customized version of http://www.thingiverse.com/thing:2379453 Created with Customizer! http://www.thingiverse.com/apps/customizer/run?thing_id=2379453

Topics: Signs & Logos, customized, thingiverse, stl

2
2.0

Jun 30, 2018
06/18

by
F. Götze; A. N. Tikhomirov

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Let $\mathbf X=(X_{jk})$ denote a $n\times p$ random matrix with entries $X_{jk}$, which are independent for $1\le j\le n, 1\le k\le p$. Let $n,p$ tend to infinity such that $\frac np=y+O(n^{-1})\in(0,1]$. For those values of $n,p$ we investigate the rate of convergence of the expected spectral distribution function of the matrix $\mathbf W=\frac1{ p}\mathbf X\mathbf X^*$ to the Marchenko-Pastur law with parameter $y$. Assuming the conditions $\mathbf E X_{jk}=0$, $\mathbf E X_{jk}^2=1$ and $...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1412.6284

3
3.0

Jun 29, 2018
06/18

by
Friedrich Götze; Alexey Naumov; Alexander Tikhomirov; Dmitry Timushev

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We consider a random symmetric matrix ${\bf X} = [X_{jk}]_{j,k=1}^n$ with upper triangular entries being i.i.d. random variables with mean zero and unit variance. We additionally suppose that $\mathbb E |X_{11}|^{4 + \delta} =: \mu_{4+\delta} < \infty$ for some $\delta > 0$. The aim of this paper is to significantly extend recent result of the authors [18] and show that with high probability the typical distance between the Stieltjes transform of the empirical spectral distribution (ESD)...

Topics: Probability, Spectral Theory, Mathematics

Source: http://arxiv.org/abs/1602.03073

2
2.0

Jun 29, 2018
06/18

by
Friedrich Götze; Denis Koleda; Dmitry Zaporozhets

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Consider a random polynomial $$ G(z):=\xi_0+\xi_1z+\dots+\xi_nz^n,\quad z\in\mathbb{C}, $$ where $\xi_0,\xi_1,\dots,\xi_{n}$ are independent real-valued random variables with probability density functions $f_0,\dots,f_n$. We give an explicit formula for the mixed $(k,l)$-correlation function $\rho_{k,l}:\mathbb{R}^k\times\mathbb{C}_+^l \to\mathbb{R}_+$ between $k$ real and $l$ complex zeros of $G_n$.

Topics: Complex Variables, Probability, Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1610.03610

3
3.0

Jun 28, 2018
06/18

by
S. G. Bobkov; G. P. Chistyakov; F. Götze

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Optimal stability estimates in the class of regularized distributions are derived for the characterization of normal laws in Cramer's theorem with respect to relative entropy and Fisher information distance.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1512.03571

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49

Sep 18, 2013
09/13

by
F. Götze; A. Naumov; A. Tikhomirov

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In this paper we study ensembles of random symmetric matrices $\X_n = {X_{ij}}_{i,j = 1}^n$ with dependent entries such that $\E X_{ij} = 0$, $\E X_{ij}^2 = \sigma_{ij}^2$, where $\sigma_{ij}$ may be different numbers. Assuming that the average of the normalized sums of variances in each row converges to one and Lindeberg condition holds we prove that the empirical spectral distribution of eigenvalues converges to Wigner's semicircle law.

Source: http://arxiv.org/abs/1211.0389v2

4
4.0

Jun 28, 2018
06/18

by
Friedrich Götze; Alexey Naumov; Alexander Tikhomirov

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We consider a random symmetric matrix ${\bf X} = [X_{jk}]_{j,k=1}^n$ in which the upper triangular entries are independent identically distributed random variables with mean zero and unit variance. We additionally suppose that $\mathbb E |X_{11}|^{4 + \delta} =: \mu_4 < \infty$ for some $\delta > 0$. Under these conditions we show that the typical distance between the Stieltjes transform of the empirical spectral distribution (ESD) of the matrix $n^{-\frac{1}{2}} {\bf X}$ and Wigner's...

Topics: Probability, Spectral Theory, Mathematics

Source: http://arxiv.org/abs/1510.07350

2
2.0

Jun 29, 2018
06/18

by
Vasili Bernik; Friedrich Götze; Anna Gusakova

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Let $\varphi:\mathbb{R}\rightarrow \mathbb{R}$ be a continuously differentiable function on an interval $J\subset\mathbb{R}$ and let $\boldsymbol{\alpha}=(\alpha_1,\alpha_2)$ be a point with algebraically conjugate coordinates such that the minimal polynomial $P$ of $\alpha_1,\alpha_2$ is of degree $\leq n$ and height $\leq Q$. Denote by $M^n_\varphi(Q,\gamma, J)$ the set of such points $\boldsymbol{\alpha}$ such that $|\varphi(\alpha_1)-\alpha_2|\leq c_1 Q^{-\gamma}$. We show that for a real $0

Topics: Number Theory, Mathematics

Source: http://arxiv.org/abs/1608.00873

78 RPMs and Cylinder Recordings

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20

Oct 4, 2019
10/19

by
Nene-Quartett; Fischer; Bremen; August Freudenthal; Carl Gotze

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Performer: Nene-Quartett Writer: Fischer; Bremen; August Freudenthal; Carl Gotze Text von August Freudenthal, Musik von Carl Gotze, Op 160. Digitized at 78 revolutions per minute. Four stylii were used to transfer this record. They are 3.8mil truncated conical, 2.3mil truncated conical, 2.8mil truncated conical, 3.3mil truncated conical. The preferred versions suggested by an audio engineer at George Blood, L.P. have been copied to have the more friendly filenames. Matrix number: 944441 M...

Topics: 78rpm, Popular Music

Source: 78

Performer: Marianne Alfermann; Richard Bitterauf Writer: Karl Götze Duett:; Sopran und; Bariton mit Orchesterbegleitung. Digitized at 78 revolutions per minute. Four stylii were used to transfer this record. They are 3.5mil truncated eliptical, 2.3mil truncated conical, 2.8mil truncated conical, 3.3mil truncated conical. These were recorded flat and then also equalized with Turnover: 500.0. The preferred versions suggested by an audio engineer at George Blood, L.P. have been copied to have the...

Topics: 78rpm, Popular Music

Source: 78

3
3.0

Jun 28, 2018
06/18

by
Friedrich Götze; Dzianis Kaliada; Dmitry Zaporozhets

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We give an explicit formula for the correlation functions of real zeros of a random polynomial with arbitrary independent continuously distributed coefficients.

Topics: Probability, Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1510.00025

3
3.0

Jun 28, 2018
06/18

by
Oliver Götze; Johannes Richter

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While the existence of a spin-liquid ground state of the spin-1/2 kagome Heisenberg antiferromagnet (KHAF) is well established, the discussion of the effect of an interlayer coupling (ILC) by controlled theoretical approaches is still lacking. Here we study this problem by using the coupled-cluster method to high orders of approximation. We consider a stacked KHAF with a perpendicular ILC $J_\perp$, where we study ferro- as well as antiferromagnetic $J_\perp$. We find that the spin-liquid...

Topics: Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1510.04898

2
2.0

Jun 28, 2018
06/18

by
Friedrich Götze; Alexey Naumov; Alexander Tikhomirov

texts

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We consider a random symmetric matrix ${\bf X} = [X_{jk}]_{j,k=1}^n$ with upper triangular entries being independent identically distributed random variables with mean zero and unit variance. We additionally suppose that $\mathbb E |X_{11}|^{4 + \delta} =: \mu_{4+\delta} < C$ for some $\delta > 0$ and some absolute constant $C$. Under these conditions we show that the typical Kolmogorov distance between the empirical spectral distribution function of eigenvalues of $n^{-1/2} {\bf X}$ and...

Topics: Probability, Spectral Theory, Mathematics

Source: http://arxiv.org/abs/1511.00862

9
9.0

Jun 30, 2018
06/18

by
Friedrich Götze; Dzianis Kaliada; Dmitry Zaporozhets

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For a region $\Omega \subset\mathbb{C}$ denote by $\Psi(Q;\Omega)$ the number of complex algebraic numbers in $\Omega$ of degree $\leq n$ and naive height $\leq Q$. We show that $$ \Psi(Q;\Omega)=\frac{Q^{n+1}}{2\zeta(n+1)}\int_\Omega\psi(z)\,\nu(dz)+O\left(Q^n \right),\quad Q\to\infty, $$ where $\nu$ is the Lebesgue measure on the complex plane and the function $\psi$ will be given explicitly.

Topics: Mathematics, Probability, Number Theory

Source: http://arxiv.org/abs/1410.3623

2
2.0

Jun 30, 2018
06/18

by
Mindaugas Bloznelis; Friedrich Götze

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In an affiliation network vertices are linked to attributes and two vertices are declared adjacent whenever they share a common attribute. For example, two customers of an internet shop are called adjacent if they have purchased the same or similar items. Assuming that each newly arrived customer is linked preferentially to already popular items we obtain a preferred attachment model of an evolving affiliation network. We show that the network has a scale-free property and establish the...

Topics: Physics, Probability, Mathematics, Data Analysis, Statistics and Probability, Physics and Society

Source: http://arxiv.org/abs/1401.7560

4
4.0

Jun 29, 2018
06/18

by
V. Bernik; F. Götze; A. Gusakova

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We show that for any sufficiently large integer $Q$ and a real $0\leq\lambda\leq\frac34$ there exists a value $c(n,f,J)>0$ such that all strips $L(Q,\lambda)=\{(x,y):|y-f(x)|

Topics: Number Theory, Mathematics

Source: http://arxiv.org/abs/1602.01631

3
3.0

Jun 30, 2018
06/18

by
Friedrich Götze; Alexey Naumov; Alexander Tikhomirov

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In this paper we consider the product of two independent random matrices $\mathbb X^{(1)}$ and $\mathbb X^{(2)}$. Assume that $X_{jk}^{(q)}, 1 \le j,k \le n, q = 1, 2,$ are i.i.d. random variables with $\mathbb E X_{jk}^{(q)} = 0, \mathbb E (X_{jk}^{(q)})^2 = 1$. Denote by $s_1, ..., s_n$ the singular values of $\mathbb W: = \frac{1}{n} \mathbb X^{(1)} \mathbb X^{(2)}$. We prove the central limit theorem for linear statistics of the squared singular values $s_1^2, ..., s_n^2$ showing that the...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1412.3314

3
3.0

Jun 30, 2018
06/18

by
Friedrich Götze; Alexey Naumov; Alexander Tikhomirov

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We consider the products of $m\ge 2$ independent large real random matrices with independent vectors $(X_{jk}^{(q)},X_{kj}^{(q)})$ of entries. The entries $X_{jk}^{(q)},X_{kj}^{(q)}$ are correlated with $\rho=\mathbb E X_{jk}^{(q)}X_{kj}^{(q)}$. The limit distribution of the empirical spectral distribution of the eigenvalues of such products doesn't depend on $\rho$ and equals to the distribution of $m$th power of the random variable uniformly distributed on the unit disc.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1404.7013

4
4.0

Jun 29, 2018
06/18

by
S. G. Bobkov; G. P. Chistyakov; F. Götze

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We explore properties of the $\chi^2$ and more general R\'enyi (Tsallis) distances to the normal law. In particular we provide necessary and sufficient conditions for the convergence to the normal law in the central limit theorem using these distances. Moreover, we derive exact rates of convergence in these distances with respect to an increasing number of summands.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1608.01805

5
5.0

Jun 30, 2018
06/18

by
V. Bernik; F. Götze; A. Gusakova

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Let $\varphi:\mathbb{R}\rightarrow \mathbb{R}$ be a continuously differentiable function on an interval $J\subset\mathbb{R}$ and let $\boldsymbol{\alpha}=(\alpha_1,\alpha_2)$ be a point with algebraic conjugate integer coordinates of degree $\leq n$ and of height $\leq Q$. Denote by $\tilde{M}^n_\varphi(Q,\gamma, J)$ the set of points $\boldsymbol{\alpha}$ such that $|\varphi(\alpha_1)-\alpha_2|\leq c_1 Q^{-\gamma}$. In this paper we show that for a real $0

Topics: Number Theory, Mathematics

Source: http://arxiv.org/abs/1704.03542

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46

Nov 24, 2010
11/10

by
Gotze, August Woldemar, 1876-1946; Volz, Hans

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32
32

Sep 19, 2013
09/13

by
G. Foffi; W. Gotze; F. Sciortino; P. Tartaglia; Th. Voigtmann

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We report extensive molecular-dynamics simulation results for binary mixtures of hard spheres for different size disparities and different mixing percentages,for packing fractions up to 0.605 and over a characteristic time interval spanning up to five orders in magnitude. We explore the changes in the evolution of glassy dynamics due to mixing and discover two opposite scenarios: for large size disparity, increasing the mixing percentage of small particles leads to a speed-up of long-time...

Source: http://arxiv.org/abs/cond-mat/0303652v1

0
0.0

Jan 20, 2021
01/21

by
Steven Götze (StevenG84)

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Einfacher Türgriff mit seitlicher Verschraubung für viele Anwendungsbereiche nutzbar.

Topics: Outdoor & Garden, stl, thingiverse

2
2.0

Jun 30, 2018
06/18

by
Friedrich Götze; Denis Koleda; Dmitry Zaporozhets

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Given a polynomial $q(z):=a_0+a_1z+\dots+a_nz^n$ and a vector of positive weights $\mathbf{w}=(w_0, w_1,\dots,w_n)$, define the $\mathbf{w}$-weighted $l_p$-norm of $q$ as $$ l_{p,\mathbf{w}}[q]:=\left(\sum_{k=0}^{n}|w_k a_k|^p\right)^{1/p},\quad p\in[1,\infty]. $$ Define the $\mathbf{w}$-weighted $l_p$-norm of an algebraic number to be the $\mathbf{w}$-weighted $l_p$-norm of its minimal polynomial. For non-negative integers $k,l$ such that $k+2l\leq n$ and a Borel subset $B\subset...

Topics: Classical Analysis and ODEs, Probability, Complex Variables, Number Theory, Mathematics

Source: http://arxiv.org/abs/1703.02289

4
4.0

Jun 30, 2018
06/18

by
Friedrich Götze; Dmitry Zaporozhets

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Consider a random polynomial $$ G_Q(x)=\xi_{Q,n}x^n+\xi_{Q,n-1}x^{n-1}+...+\xi_{Q,0} $$ with independent coefficients uniformly distributed on $2Q+1$ integer points $\{-Q, ..., Q\}$. Denote by $D(G_Q)$ the discriminant of $G_Q$. We show that there exists a constant $C_n$, depending on $n$ only such that for all $Q\ge 2$ the distribution of $D(G_Q)$ can be approximated as follows $$ \sup_{-\infty\leq a\leq b\leq\infty}|\mathbb{P}(a\leq \frac{D(G_Q)}{Q^{2n-2}}\leq b)-\int_a^b\varphi_n(x)\,...

Topics: Mathematics, Probability, Number Theory

Source: http://arxiv.org/abs/1407.6388

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2.0

Jun 30, 2018
06/18

by
Michael Baake; Friedrich Götze; Christian Huck; Tobias Jakobi

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In this paper, we explore the radial projection method for locally finite point sets and provide numerical examples for different types of order. The main question is whether the method is suitable to analyse order in a quantitive way. Our findings indicate that the answer is affermative. In this context, we also study local visibility conditions for certain types of aperiodic point sets.

Topics: Mathematics, Metric Geometry, Dynamical Systems

Source: http://arxiv.org/abs/1402.2818

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0.0

Apr 17, 2021
04/21

by
Benjamin Götze (BennyG)

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Designed for use with 40mm fan ducts. I also had to adjust the fan speed, because 100% with the fan would cool the hot end too much. Set the fan speed if you notice an unstable temperature. Connecting elements used: 1 - M3 x 30mm 1 - Nut M3 4 - Screws 5mm

Topics: thingiverse, 3D Printer Accessories, stl

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Sep 21, 2013
09/13

by
S. G. Bobkov; G. P. Chistyakov; F. Götze

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Convergence to stable laws in relative entropy is established for sums of i.i.d. random variables.

Source: http://arxiv.org/abs/1104.4360v1

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2.0

Jun 30, 2018
06/18

by
F. Götze; A. Reshetenko

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We study asymptotic expansions in free probability. In a class of classical limit theorems Edgeworth expansion can be obtained via a general approach using sequences of "influence" functions of individual random elements described by vectors of real parameters $(\varepsilon_1,..., \varepsilon_n)$, that is by a sequence of functions $h_n(\varepsilon_1,..., \varepsilon_n;t)$, $|\varepsilon_j| \leq \frac 1 {\sqrt n}$, $j=1,...,n$, $t\in {\mathbb R}$ (or ${\mathbb C}$) which are smooth,...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1408.1360

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2.0

Jun 30, 2018
06/18

by
F. Götze; A. Yu. Zaitsev

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A multidimensional version of the results of Koml\'os, Major and Tusn\'ady for sums of independent random vectors with finite exponential moments is obtained in the particular case where the summands have smooth distributions which are close to Gaussian ones. The bounds obtained reflect this closeness. Furthermore, the results provide sufficient conditions for the existence of i.i.d. vectors $X_1, X_2,\dots$ with given distributions and corresponding i.i.d. Gaussian vectors $Y_1, Y_2,\dots$...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1402.1420

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6.0

Jun 27, 2018
06/18

by
R. F. Bishop; P. H. Y. Li; O. Götze; J. Richter; C. E. Campbell

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We use the coupled cluster method implemented to high orders of approximation to investigate the frustrated spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$ antiferromagnet on the honeycomb lattice with isotropic Heisenberg interactions of strength $J_{1} > 0$ between nearest-neighbor pairs, $J_{2}>0$ between next-nearest-neighbor pairs, and $J_{3}>0$ between next-next-neareast-neighbor pairs of spins. In particular, we study both the ground-state (GS) and lowest-lying triplet...

Topics: Condensed Matter, Strongly Correlated Electrons

Source: http://arxiv.org/abs/1504.02275

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2.0

Jun 30, 2018
06/18

by
F. Götze; H. Kösters; A. Tikhomirov

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We investigate the universality of singular value and eigenvalue distributions of matrix valued functions of independent random matrices and apply these general results in several examples. In particular we determine the limit distribution and prove universality under general conditions for singular value and eigenvalue distributions of products of independent matrices from spherical ensembles.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1408.1732

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2.0

Jun 28, 2018
06/18

by
F. Götze; A. Tikhomirov

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This paper extends a previous bound of order $O(n^{-1})$ of the authors (arXiv:1405.7820[math.PR]), for the rate of convergence in Kolmogorov distance of the expected spectral distribution of a Wigner random matrix ensemble to the semicircular law. Here we relax the moment conditions for entries of the Wigner matrices from order $8$ to order $4+ \epsilon$ for an arbitrary small $\epsilon>0$.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1511.03692

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4.0

Jun 30, 2018
06/18

by
Gennadii Chistyakov; Friedrich Götze

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We prove an expansion for densities in the free CLT and apply this result to an expansion in the entropic free central limit theorem assuming a moment condition of order four for the free summands.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1701.04352